What a square root is
The square root of a number is the value that, multiplied by itself, gives that number. The square root of 72 is 8.485281374, because that number squared is 72.
Only zero and positive numbers have real square roots. A negative number has no real answer, so the calculator refuses it.
Simplified surds
Whole numbers that are not perfect squares can often be written with part of the root taken outside. 72 is 36 x 2, so the square root is 6 times the square root of 2.
This keeps the answer exact. The decimal is only an approximation of the same value.
Worked example
The square root of 72 is 8.485281374, and its simplified surd form is 6 times the square root of 2.
The square root of 144 is exactly 12, because 12 x 12 = 144, so 144 is a perfect square.
Inputs for the square root calculator
Number
Zero or a positive number. Negative values have no real square root and are refused.
CALCULATOR QUESTIONS
Square root calculator questions
What is the square root of 72?
8.485281374, or exactly 6 times the square root of 2.
What is a perfect square?
A number whose square root is a whole number, such as 144, 169 or 196.
Why can't I take the square root of a negative number?
No real number multiplied by itself gives a negative result. The answer would need an imaginary number.
How do I simplify a surd?
Find the largest square factor of the number, take its root outside, and leave the rest under the root sign.